Page:Scientific Memoirs, Vol. 1 (1837).djvu/535

effect obtainable will depend on the value of $f$ or of the friction. By differentiating the second member with respect to $n$, we shall have for this maximum $n={\frac {E-fr'}{2fr}}$.

The bar which was used in the experiments of article 9 weighed 14½ lbs. Being adapted to any moveable apparatus, the friction it occasions would amount at most to ½ lb. It has been found by experiments: $E=283.6$, $r'=20$, $r=1$, and $f={\frac {1}{2}}$, thus $n=273.6$; that is to say, there would be the greatest possible advantage in employing about 273 bars wound round with helices of the same size. This number varies with the size of the plates: for a surface $m$, we have $n={\frac {mE-fr'}{2fmr}}$. In short the magnetic power available for practical purposes is ${\frac {nE}{nr+r'}}-nf={\frac {(E-fr')^{2}}{(E+fr')2r}}$.

15.

In employing a voltaic battery, the œconomical effect will be diminished, unless at the same time the helices united in the same wire be multiplied; for Mr. Faraday has proved by the experiments reported in the articles 990, &c. of the Eighth Series of his Researches, that the same quantity of electricity passes through a voltaic battery of any number of pairs of plates which traverses a single pair of the same size. The quantity of gas disengaged at the surface of each plate of the battery is the same as at the surface of a single pair; this at first sight appears astonishing, and seems to contradict numerous experiments which have been made upon the pile; for every one knows that the quantity of gas disengaged by the decomposing apparatus, and at the same time the deviation of the needle, increase up to a certain point, by multiplying the number of plates.

In considering the formula $F={\frac {n'E}{n'r'+r}}$ where $n'$ represents the number of pairs of plates, $r'$ the resistance of each pair, and $r$ that of the connecting wire, or of the body which we wish to decompose, we must suppose that in the experiments of Mr. Faraday (990.) the connecting wire of the battery and of the single pair of plates were so short that its resistance $r$ might be entirely neglected in relation to $n'r'$. We should not have obtained this striking result if we had employed a connecting wire of any considerable length, and still less if we had closed the circuits of the pair of plates and of the battery by any decomposing apparatus. Mr. Faraday has established a very exact distinction between the quantity and intensity of electricity set in motion. The first may be measured in different ways; but it will be difficult to find an exact measure for its intensity, nevertheless this would be very necessary for completing the theory. In admitting the important law